# Hohman orbits University Physics I

1. Apr 11, 2009

### THTremere

1. The problem statement, all variables and given/known data
Im not sure how to solve this one...

Hohmann orbits are the lowest energy orbits to move things from one planet to another in a solar system. In order to send something from the Earth to another planet in the solar system, you launch the object when the Earth and the other planet are laid out at the opposite ends of the major axis of an ellipse which has the sun at one focus. Let's see how useful Hohmann orbits can be launching something from the Earth to Mars. Take th distance from the Earth to the sun to be 1.5x10^11m, and from Mars to the sun to be 2.3x10^11m. The mass of the sun is 2x10^30kg.
a) Let's say that the total energy required for the Hohmann orbit around the sun from the Earth to Mars for a probe is -3x10^11 J. What is the mass of a probe that can achieve this energy requirement?

Im thinking it involves setting up E tot= K + U(gravitational) But Im not sure really where to go from there!! I dont have a velocity...maybe use conservation of angular momentum....Anyway Im not sure how to even set up this problem it seems. Any help in the right direction would be greatly appreciated.

2. Relevant equations
E=K+U
E=1/2mV^2 - GMm/r
L=L (angular momentum)

3. The attempt at a solution
Im not sure how to set this one up....If I could get a shove in the right direction I could really attempt this :)

I tried this ... mp(mass of the probe)=E-total/(1/2V^2-GM(earth)/r(earth)-GM(sun)/R(sun)-GM(mars)/r(mars)
I doubt that is correct though...